the window is so tall that the title bar at the top of the window is invisible unless you either resize the tray or the window testing on Windows 7. Would it be difficult to deduct the size of the system tray at the bottom?

I think it's actually quite some work, probably not worth the effort. AFAIR the taskbar can switch places or can be hidden completely, and there's of course also macOS and Linux to be taken into account where the issue would have to be fixed as well. Then there's the problem that Linux and macOS often have title bars which also would have to be taken into account. It's quite a lot of work for very little gain IMHO.